A new family of time integration methods for heat conduction problems using numerical Green's functions (Q835514)

A class of time integration methods for linear heat conduction equation based on numerical Green's function is presented. The main contributions of this paper are the use of modified Green's matrix which generates a robust method called ``Modified Explicit Green's Approach''. An optimized family of Runge-Kutta schemes to compute the Green's matrix or modified Green's matrix is presented. The effectiveness of the present methodology is demonstrated by analyzing two numerical examples.